Using the Alkali.ne Rydberg Calculator (ARC) package [1]}, \(H\)  can be easily calculated and diagonalized. To find the effective blockade strength (defined below), we diagonalized \(H\) , taking into account all Rydberg states with principle quantum number \(104 \le n \le 110\)  and with orbital quantum number \(l \le 3\) . The eigenvalues for \(R\)  between 3\(\mu \) m and 12\(\mu \) m are shown in Fig. REF (a), with the color indicating the squared overlap between the corresponding eigenstate and \(\mathinner {|{rr}\rangle }\) . It can be seen that, contrary to the simple model in Fig. REF (a), there are several eigenstates \(\mathinner {|{\varphi _i}\rangle }\)  with a significant overlap with \(\mathinner {|{rr}\rangle }\) . Since the effects of a finite blockade strength are well approximated through an ac-Stark shift of the \(\mathinner {|{W}\rangle }\)  state (see Appendix ), we define the effective blockade strength \(B_{\mathrm {eff}}\)  as the blockade strength which correctly reproduces the ac-Stark shift of \(\mathinner {|{W}\rangle }\)  coming from the coupling to all \(\mathinner {|{\varphi _i}\rangle }\) . This effective blockade strength has been introduced under the name frequency shift factor before [2]}. \(B_{\mathrm {eff}}\)  can be calculated as
\(\frac{1}{B_{\mathrm {eff}}} = \frac{2}{\Omega ^2}\sum _i \frac{|\mathinner {\langle {W|H_{\mathrm {laser}}|\varphi _i}\rangle }|^2}{\Delta _i}\) 
